One of the hardest tasks any gardener faces is replacing old fence posts. Over time the effects of rot takes it tole and frequently a storm will then snap the posts.
I have used many different methods to replace the posts in the past and have on occasion even managed to chisel out the old post and fit a new one in the existing concrete. The metal posts never seem to drive into the ground freely and often seem to get damaged if they hit a rock on the way down.
I tend to favour removing the old post and concrete if necessary and starting again from sctratch.
One technique I have used recently is use simple machinery to lift the posts out and reduce the amount of digging required. When we lost two posts to the most recent storm I found the I could dig down a small amount and drill trough the wood. I then fed a D link bike lock through the wood and locked the end to provide a strong anchorage point. A cable puller / ratchet was then attached to the lock and the post pulled out.